The simple answer is that PI is what falls out when you study circles. If I had a circle that is 1 foot in diameter, then the circumference (or perimeter) is PI feet. The numerical value of PI wasn't chosen at random, it was found. As for the area of a circle, the perimeter of any object has a relationship to its area. So, PI again becomes important.
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The area of a circle, in terms of pie, with a diameter of 36 is: about 324pi
In order to find the diameter of a circle if you have the area is to rearrange the formula for the area of a circle to put diameter as the unknown, like so: PIE*d = Area of a Circle d = (Area of a Circle) / PIE Therefore if the area of your circle is 40cm, 40/PIE = 12.73cm and that's the diameter.
This circle's area would be 78.54 units squared.
Circumference of a circle = diameter*pi
The circumference of a circle with an area of 121 pie yards squared (380.13 yards2) is: 69.1 yards